Average Error: 0.0 → 0.0
Time: 12.4s
Precision: 64
Internal Precision: 128
\[e^{re} \cdot \sin im\]
↓
\[\sin im \cdot e^{re}\]

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[e^{re} \cdot \sin im\]

  2. Final simplification0.0

    \[\leadsto \sin im \cdot e^{re}\]

Reproduce

herbie shell --seed 2019016 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))

Details

Time bar (total: 11.7s)Debug log

sample129.0ms

Algorithm
intervals
Results
328×(pre true 80)
218×(body real 80)
53×(body real 1280)
31×(body real 640)
13×(body real 320)
13×(body real 160)

simplify4.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
4.0ms
(* (exp re) (sin im))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (exp re) (sin im))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
3×add-cube-cbrt
3×associate-*l*
3×associate-*r*
3×add-cbrt-cube
3×*-un-lft-identity
3×pow1
3×add-sqr-sqrt
2×add-exp-log
1×add-log-exp
1×log1p-expm1-u
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-prod-down
1×expm1-log1p-u
Counts
1 → 19
Calls
1 calls:
Slowest
9.0ms
(* (exp re) (sin im))

series44.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
44.0ms
(* (exp re) (sin im))

simplify397.0ms

Counts
11 → 22
Calls
11 calls:
Slowest
298.0ms
(+ (* 1/2 (* (pow re 2) im)) (+ (* re im) im))
82.0ms
(* (* (* (exp re) (exp re)) (exp re)) (* (* (sin im) (sin im)) (sin im)))
4.0ms
(+ re (log (sin im)))
3.0ms
(* (exp re) (sin im))
2.0ms
(* (sin im) (exp re))

prune166.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (exp re))
0.0b
(cbrt (exp re))
0.0b
(cbrt (exp re))
0.0b
(* (cbrt (exp re)) (cbrt (exp re)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
11×add-cube-cbrt
11×*-un-lft-identity
11×add-sqr-sqrt
9×pow1
7×pow1/3
6×add-exp-log
6×associate-*l*
6×associate-*r*
4×add-log-exp
4×log1p-expm1-u
4×add-cbrt-cube
4×expm1-log1p-u
2×pow-prod-up
2×pow-prod-down
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-plus
1×pow2
Counts
4 → 69
Calls
4 calls:
Slowest
10.0ms
(* (cbrt (exp re)) (cbrt (exp re)))
1.0ms
(cbrt (exp re))
1.0ms
(cbrt (exp re))
1.0ms
(cbrt (exp re))

series570.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(* (cbrt (exp re)) (cbrt (exp re)))
151.0ms
(cbrt (exp re))
133.0ms
(cbrt (exp re))
127.0ms
(cbrt (exp re))

simplify241.0ms

Counts
41 → 81
Calls
41 calls:
Slowest
57.0ms
(+ (* 2/3 re) (+ (* 2/9 (pow re 2)) 1))
35.0ms
(+ (* 1/3 re) (+ (* 1/18 (pow re 2)) 1))
35.0ms
(+ (* 1/3 re) (+ (* 1/18 (pow re 2)) 1))
35.0ms
(+ (* 1/3 re) (+ (* 1/18 (pow re 2)) 1))
7.0ms
(pow (pow (exp re) 2) 1/3)

prune817.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cbrt (cbrt (exp re))) (cbrt (cbrt (exp re))))
0.0b
(cbrt (exp re))
0.0b
(cbrt (exp re))
0.0b
(cbrt (exp re))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
27×cbrt-prod
13×add-cube-cbrt
13×*-un-lft-identity
13×add-sqr-sqrt
9×associate-*l*
9×associate-*r*
9×pow1
7×pow1/3
6×add-exp-log
4×add-log-exp
4×log1p-expm1-u
4×add-cbrt-cube
4×expm1-log1p-u
2×pow-prod-up
2×pow-prod-down
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×pow-plus
1×pow2
Counts
4 → 75
Calls
4 calls:
Slowest
14.0ms
(* (cbrt (cbrt (exp re))) (cbrt (cbrt (exp re))))
1.0ms
(cbrt (exp re))
1.0ms
(cbrt (exp re))
1.0ms
(cbrt (exp re))

series531.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
154.0ms
(* (cbrt (cbrt (exp re))) (cbrt (cbrt (exp re))))
142.0ms
(cbrt (exp re))
123.0ms
(cbrt (exp re))
111.0ms
(cbrt (exp re))

simplify314.0ms

Counts
47 → 87
Calls
47 calls:
Slowest
73.0ms
(+ (* 1/3 re) (+ (* 1/18 (pow re 2)) 1))
69.0ms
(+ (* 1/3 re) (+ (* 1/18 (pow re 2)) 1))
36.0ms
(+ (* 2/9 re) (+ (* 2/81 (pow re 2)) 1))
34.0ms
(+ (* 1/3 re) (+ (* 1/18 (pow re 2)) 1))
5.0ms
(exp (* 1/3 re))

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cbrt (cbrt (exp re))) (cbrt (cbrt (exp re))))
0.0b
(* (cbrt (cbrt (exp re))) (cbrt (cbrt (exp re))))
0.0b
(* (cbrt (cbrt (exp re))) (cbrt (cbrt (exp re))))
0.0b
(cbrt (exp re))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
57×cbrt-prod
27×associate-*l*
27×associate-*r*
23×add-cube-cbrt
23×*-un-lft-identity
23×add-sqr-sqrt
19×pow1
13×pow1/3
10×add-exp-log
6×pow-prod-up
6×pow-prod-down
4×add-log-exp
4×log1p-expm1-u
4×add-cbrt-cube
4×expm1-log1p-u
3×cbrt-unprod
3×*-commutative
3×prod-exp
3×pow-plus
3×pow2
Counts
4 → 121
Calls
4 calls:
Slowest
12.0ms
(* (cbrt (cbrt (exp re))) (cbrt (cbrt (exp re))))
11.0ms
(* (cbrt (cbrt (exp re))) (cbrt (cbrt (exp re))))
11.0ms
(* (cbrt (cbrt (exp re))) (cbrt (cbrt (exp re))))
1.0ms
(cbrt (exp re))

series522.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
144.0ms
(* (cbrt (cbrt (exp re))) (cbrt (cbrt (exp re))))
140.0ms
(cbrt (exp re))
120.0ms
(* (cbrt (cbrt (exp re))) (cbrt (cbrt (exp re))))
118.0ms
(* (cbrt (cbrt (exp re))) (cbrt (cbrt (exp re))))

simplify340.0ms

Counts
93 → 133
Calls
93 calls:
Slowest
68.0ms
(+ (* 1/3 re) (+ (* 1/18 (pow re 2)) 1))
50.0ms
(+ (* 2/9 re) (+ (* 2/81 (pow re 2)) 1))
46.0ms
(+ (* 2/9 re) (+ (* 2/81 (pow re 2)) 1))
38.0ms
(+ (* 2/9 re) (+ (* 2/81 (pow re 2)) 1))
7.0ms
(pow (pow (exp re) 2) 1/9)

prune2.0s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes275.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch1.0ms

end0.0ms

sample4.0s

Algorithm
intervals
Results
10646×(pre true 80)
6939×(body real 80)
1533×(body real 1280)
1208×(body real 640)
660×(body real 320)
306×(body real 160)